A Network Attached Storage (NAS) is something you may be interested in. There are several plug and play products available from companies such as Synology, Western Digital, etc. As well, there are a couple options for DIY'ers such as Freenas, Unraid, etc.
I have a Freenas machine that I built running in our home that I am able to access over the network, through any of our devices as well as remotely. As well, I've set up the computers in our home to back up to this NAS often. This is made up of spare computer hardware that I had laying around, that I've been slowly upgrading and replacing. I chose to house it in an Antec P100 case (plenty of hard drive trays, quiet, and plenty of fan / cooler mounting options).
The requirements for a machine to run Freenas is pretty reasonable. Looking at Freenas's website:
- Multicore 64-bit processor (Intel strongly recommended)
- 8GB Boot Drive (USB Flash Drive suffices)
- 8GB
- At least 1 direct attached disk (Hardware RAID strongly discouraged)
- One physical network port
I've ran both Intel and AMD Freenas machines and honestly haven't noticed a difference (I'm sure there is, but as a user, I haven't seen a difference in my tasks). It is encouraged to use hard drives rated for NAS (WD Red, Seagate Ironwolf, etc.) as the manufacture warranty's for such use. I've used spare hard drives that I've had laying around for my personal machines and haven't had issues so far. I am in the process of saving up for WD Red drives to replace my current set of drives.
There may be better options that are out there, but for me and my use-cases, Freenas has been perfect.